“Based on my conversations with [British] prime minister Cameron and with [German] chancellor Merkel and here today, I’m absolutely confident the EU will work in a pragmatic and cooperative fashion to ensure that the UK transition is orderly”, he said.

“No one has an interest in protracted, adversarial negotiations”, he said.

Obama spoke alongside EU Council chief Donald Tusk and European Commission head Jean-Claude Juncker.

Calling them by their first names, he said the EU and US would continue to work hand-in-hand on the world stage.

“The security of America and Europe is indivisible … Europe is an indispensable partner around the globe”, he said.

He listed the main areas of cooperation, such as Russia sanctions, counter-terrorism, free trade talks, and climate change.

But with populist politicians on the rise in the US and in the EU, he added that both Washington and Brussels must address the “fears” of poorer people who were “left behind” by globalisation.

“Our governments, including in the EU, cannot be remote institutions. We have to be responsive, move quickly, with minimal bureaucracy to deliver economic growth”, Obama said.

Tusk told press that “it's important to send a legible signal to the whole world that Brexit is, albeit sad and important, just one incident and not the start of a process”.

“To all our opponents, who want to see a repeat of Brexit, I would like to clearly say that you won’t see on your screens the words: ‘To be continued’,” he added.

Juncker said the UK and the EU are bound together by shared “feelings” in “all aspects of life”.

He said that it would remain a “strong ally”, but he warned Britain that it would not get access to the single market unless it let in migrant workers from Europe.

Speaking later on Friday after a meeting with Polish prime minister Beata Szydlo, the outgoing British leader, David Cameron, said: “Great Britain might be leaving the EU, but we are not turning our back on Europe or on the defence and security of Europe”.

The EU and Nato the same day signed a memorandum on closer cooperation.

Nato head Jens Stoltenberg said they would work together on “answers to hybrid threats, cyber threats and also maritime cooperation”, referring to Nato efforts to support EU anti-people smuggling operations in the Mediterranean and Aegean seas.

Tusk said it would be an “illusion” to think that the EU could “go it alone” from Nato by forming parallel military structures.

But he said the EU could “add value” to Nato. “At stake is real life. Our critical infrastructure could be attacked. Our banking systems could be hacked. Our citizens could be exposed to disinformation campaigns on social media”, he said, referring to some forms of so called hybrid warfare.

The memo envisages joint EU-Nato military exercises in 2017 and 2018 and a new action plan on future cooperation, to be drafted by Nato and by the EU foreign service by December.

The discussion of hybrid warfare refers to Russia's covert and multi-pronged attack on Ukraine.

Stoltenberg said on Friday that Nato's plan to post troops to eastern Europe and to firm up its anti-hybrid capabilities were prompted by Russia's behaviour.

"We have seen a more assertive Russia. We have seen a Russia which has been willing to use military force against sovereign nations in Europe, with aggressive actions against Ukraine, the illegal annexation of Crimea", he said.

"That’s the reason … why we are now increasing our military presence in the eastern part of the alliance."